Remember the busy Bee? The one that kept flying from the bicyclist to his home and back as he approached it?

Well, at the instant when the person finally got to his house, which way was the Bee facing? (Assume that the Bee's turns are instantaneous - that it can go from facing the house to facing the cyclist in no time.)

Could be wrong but I don't believe the bee in this problem would make an infinite number of turns. The bee flies from the biker to the house and back and forth. The biker approaches the house at a steady rate and will eventually reach the house. Another way of saying this is that the distance between the biker and the house will be zero. When this occurs the bee will have no where to fly. The bee flies for a time and then ceases to fly.

If the bee finishes its route it cannot have been comprised of an infinite number of turns. Had the biker approached the house in some kind of exponentially decaying pattern then yes the bee would fly and turn infinitely but as the problem is constructed there is only a certain time the bee has to turn in.

Posted by luke on 2003-09-07 16:44:42